A349404 The maximal coefficient in the expansion of x_1(x_1 + x_2)...(x_1 + x_2 + ... + x_n).

1, 1, 1, 2, 4, 9, 27, 96, 384, 1536, 7500, 37500, 194400, 1166400, 7563150, 52942050, 385351680, 3082813440, 24998984640, 224990861760, 2024917755840, 19051200000000, 190512000000000, 1944663768432000, 21391301452752000

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..518

Sela Fried, On the coefficients of the distinct monomials in the expansion of x1(x1+x2)...(x1+x2+...+xn), arXiv:2111.07331 [math.CO], 2021.

Mathematica

Max/@Table[Values@CoefficientRules[Times@@Array[Total@Array[x, #]&, n]], {n, 0, 12}] (* Giorgos Kalogeropoulos, Nov 16 2021 *)

Prog

(Python)
from math import prod
from sympy import symbols, Poly
def A349404(n):
    if n == 0: return 1
    s = symbols('x_0:'+str(n))
    return max(Poly(prod(sum(s[j] for j in range(i)) for i in range(1, n+1))).coeffs()) # Chai Wah Wu, Mar 30 2026

Crossrefs

Cf. A000140, A065048, A347917, A392779.

Sequence in context: A003320 A007876 A343845 * A332979 A176068 A296264

Adjacent sequences: A349401 A349402 A349403 * A349405 A349406 A349407

Keyword

nonn

Author

Sela Fried, Nov 16 2021

Status

approved